1. Field of the Invention
The present invention relates to a method of generating a mesh for process simulation.
2. Description of the Related Art
Process simulators calculate various semiconductor fabrication processes including an oxidization process, a diffusion process, an ion implantation process, etc. with a computer to predict internal physical quantities and configurations such as impurity profiles for transistors.
If transistors are optimized to make semiconductor devices exhibit best electric characteristics using a process simulator, then the cost and period of time for fabricating such semiconductor devices can be much smaller than if a prototype LSI circuit were actually produced.
With a process simulator, since various semiconductor fabrication processes are calculated by a computer, each of the processes incorporate a model equation. In LSI circuits, devices are separated by LOCOS, trenches, etc. so that the devices will not electrically affect each other. The tendency in recent years for smaller microelectronic devices requires device separation simulation for LOCOS, trenches, etc., resulting in efforts to achieve two-dimensional process simulation.
One process for calculating two-dimensional LOCOS oxidization is disclosed in xe2x80x9cSemiconductor process device simulation technologyxe2x80x9d, published by Realize Co., Ltd., pages 79-89, Part 1 xe2x80x9cProcessxe2x80x9d, Chapter 2 xe2x80x9cProcess simulationxe2x80x9d, Section 3 xe2x80x9cSimulation of two-dimensional oxidizationxe2x80x9d.
According to the disclosed process, an oxidization rate is computed from an oxidant concentration, how much an Si/SiO2 interface moves is calculated at a certain time interval, and a configurational change is calculated from the displacement of the Si/SiO2 interface.
FIG. 1 of the accompanying drawings show a LOCOS structure calculated from the oxidization computation. As described above, a configurational change is calculated from the displacement of the Si/SiO2 interface. Since the displacement is produced as a result of the numerical calculation, it contains a small error, resulting in an unwanted fluctuation of the interface between the materials.
According to the process simulation, after the oxidization computation, a redistribution of the impurity distributed in Si is calculated by way of diffusion computation. In order to perform the diffusion computation, it is necessary to generate a mesh for the diffusion computation, and any unwanted fluctuations need to be reduced as much as possible for the generation of such a mesh.
Japanese patent application No. 10-082541 discloses an invention relating to a method of reducing unwanted fluctuations after the oxidization computation. According to the disclosed invention, in the LOCOS configuration shown in FIG. 1, an Si/SiO2 boundary, an SiO2/ambient boundary, and an SiO2/Si3N4 boundary are separated into blocks as shown in FIG. 2 of the accompanying drawings, and unwanted mesh points are reduced in each of the blocks thereby to reduce unwanted fluctuations.
The process according to the invention disclosed in Japanese patent application No. 10-082541 will be described below with reference to FIG. 3 of the accompanying drawings.
In step P1, region boundary line segments are acquired. The region boundary line segments include the Si/SiO2 boundary, the SiO2/ambient boundary, and the SiO2/Si3N4 boundary.
In step P2, the region boundary line segments are separated into blocks at nodes where three or more materials contact each other, as shown in FIG. 2.
In step P3, one of the blocks is selected. In step P4, simplification values xcex5 of the mesh points in the selected block are calculated. A simplification value xcex5 represents a distance that the mesh points move when the corresponding mesh point is deleted. The smaller the simplification value xcex5, the smaller the effect that the simplification has on a change in the configuration.
In step P5, a mesh point whose simplification value is the smallest in the block is selected.
In step P6, if the simplification value of the selected mesh point is smaller than a reference simplification value, then a boundary mesh point is deleted in step P7.
Since the simplification values of mesh points in the vicinity of the deleted boundary mesh point are changed, simplification values are calculated again in step P8.
The above process is repeated for each block until the simplification values of the mesh points in the block become greater than the reference simplification value.
A specific example of how the method according to the invention disclosed in Japanese patent application No. 10-082541 operates will be described below with reference to FIGS. 4(A) through 4(C) of the accompanying drawings.
A point where three materials contact each other is defined as fixed mesh point 4, and the configuration is divided into blocks as shown in FIG. 4(A).
Simplification values of mesh points 1, 2, 3 in each block are calculated as shown in FIG. 4(B).
Of the mesh points in the block, mesh point i whose simplification value is the smallest is selected, i.e., mesh point 3 shown in FIG. 4(B) is selected. If the simplification value of selected mesh point i is smaller than a predetermined reference value, then mesh point i is deleted, and simplification values of the mesh points are calculated again.
The above process is repeated for each block until the simplification values of the mesh points in the block become greater than the reference value.
One problem of the above conventional method is that it is time-consuming to simplify the configuration because it is necessary to recalculate simplification values each time a node or mesh point is deleted.
It is therefore an object of the present invention to provide a method of generating a mesh for process simulation by simplifying a configuration at a high speed for reducing the period of time required for calculations.
According to an aspect of the present invention, there is provided a method of generating a mesh for process simulation, comprising the steps of (a) acquiring region boundary line segments, (b) calculating simplification values of mesh points on each of the region boundary line segments, (c) defining a node where at least three materials contact each other on each region boundary line segment as a fixed mesh point, and setting the simplification value of the fixed mesh point to a value sufficiently larger than a reference simplification value thereby to make the fixed mesh point immovable, (d) selecting the mesh point whose simplification value is the smallest from the mesh points on each region boundary line segment, (e) if the simplification value of the selected mesh point is smaller than the reference simplification value, equally distributing the simplification value of the selected mesh point to the mesh points on both sides of and adjacent to the selected mesh point, (f) deleting the selected mesh point, and (g) repeating the steps (d) through (f) until the simplification values of all the mesh points on each region boundary line segment become greater than the reference simplification value.
According to another aspect of the present invention, there is provided a method of generating a mesh for process simulation, comprising the steps of (a) acquiring region boundary line segments, (b) calculating simplification values of mesh points on each of the region boundary line segments, (c) defining a node where at least three materials contact each other on each region boundary line segment as a fixed mesh point, and setting the simplification value of the fixed mesh point to a value sufficiently larger than a reference simplification value thereby to make the fixed mesh point immovable, (d) selecting the mesh point whose simplification value is the smallest from the mesh points on each region boundary line segment, (e) if the simplification value of the selected mesh point is smaller than the reference simplification value, distributing the simplification value of the selected mesh point to the mesh points on both sides of and adjacent to the selected mesh point, at ratios depending on the distances from the selected mesh point to the mesh points, (f) deleting the selected mesh point, and (g) repeating the steps (d) through (f) until the simplification values of all the mesh points on each region boundary line segment become greater than the reference simplification value.
According to still another aspect of the present invention, there is provided a method of generating a mesh for process simulation, comprising the steps of (a) acquiring region boundary line segments, (b) calculating simplification values of mesh points on each of the region boundary line segments, (c) defining a node where at least three materials contact each other on each region boundary line segment as a fixed mesh point, and setting the simplification value of the fixed mesh point to a value sufficiently larger than a reference simplification value thereby to make the fixed mesh point immovable, (d) selecting the mesh point whose simplification value is the smallest from the mesh points on each region boundary line segment, (e) if the simplification value of the selected mesh point is positive and smaller than the reference simplification value, equally distributing the simplification value of the selected mesh point to the mesh points on both sides of and adjacent to the selected mesh point, (f) setting the simplification value of the selected mesh point to a negative value, (g) if the simplification value of the selected mesh point is negative and smaller than the reference simplification value, saving the selected mesh point and deleting all saved mesh points altogether, and (h) repeating the steps (d) through (g) until the simplification values of the mesh points on each region boundary line segment become greater than the reference simplification value.
Each of the above methods of generating a mesh for process simulation according to the present invention is thus capable of simplifying the configuration at a high speed, reducing the generation of wasteful meshes, and shortening the period of time required for calculations.
The above and other objects, features, and advantages of the present invention will become apparent from the following description with reference to the accompanying drawings which illustrate examples of the present invention.